Estimating adding fractions with unlike denominators

• [Instructor] We are told that Tony has 2/3 of a bag of dark chocolate chips and 4/5 of a bag of white chocolate chips. Determine a reasonable estimate of the total amount of chocolate chips Tony has. So pause this video and see if you can figure out which of these choices is the best reasonable estimate of the total amount of chocolate chips.

All right, now let's work on this together. Now in the future, we will learn how to actually add something like 2/3 to 4/5, but for the sake of this exercise, we just want to get good at estimating it. And one way to estimate is to try to visualize.

So let's make, so this is a whole right over here, and then this is another whole right over there. Try to make them the same size. Now what does 2/3 look like? Well, let me divide this into three equal sections, so that is pretty close.

It's hand drawn, so it's not perfect, but I think it gets the job done. And 2/3 would be, that's 1/3 right over there and then that is 2/3 right there, and what does 4/5 looks like? Well, let's see. I can divide this into fifths, so 1/5, 2/5, 3/5, and then 4/5, and 5/5. That is pretty good.

And now what does 4/5 look like? Well, it would be 1/5, 2/5, 3/5, and then 4/5. So if we were to add these two together, do we have less than 1/2 of a bag, more than 1/2 of a bag, but less than one bag, or more than one bag?

Well, when you see even the first 2/3, where is a half? A half would have been right around there if we're talking about half of it. So 2/3 is more than a half, and then we also see that 4/5 is more than a half. If you had a half, it would have been like this far.

So you can see that you're adding two things together that are both more than a half. And if you have two halves of something, that'd be a whole, so if you have two things that are more than a half, if you add them together, you're gonna have more than a bag of chocolate chips. So I like this choice right over here.

Let's do another example. So here, we are told that a banana weighs 3/8 of a kilogram, an apple weighs 2/3 of a kilogram. Determine a reasonable estimate for the weight of both fruits.

So pause this video again and see if you can have a go at that. All right, so the key is that we need to determine a reasonable estimate. So let's actually just try to represent these again, so how could I represent 3/8 of something, of a kilogram, in this case?

Well, let me draw a rectangle here and I'm going to try to divide it into eighths, eight equal sections, so that looks about a half. Let me do it right over there. That looks like about a half, and then if I were to divide those, these would be fourths, and this is hand drawn, so it's not perfect, but it will help us understand things a bit.

So then let me divide these, and so this would get me to eighths. So I have eight sections here. One, two, three, four, five, six, seven, eight, and if I'm talking about three of those eight equal sections, I'd have 1/8, 2/8, and 3/8, so that is 3/8 right over there.

And what does 2/3 look like? So I'll do that in purple, so if this is a whole, this is a whole like that. If I divide it into three equal sections, it's going to be something like that. I could draw it a little bit better, so something like that, and so two of those three equal sections, that's 1/3, and so that is 2/3.

Now what happens if I try to add these things together? Well, one thing I could try to do to help visualize is I could take that piece there. The wholes are roughly the same length or I tried to draw them so that they are roughly the same length, and if I were to copy and paste that and move that over here, it looks like, if I were to estimate it, I'm getting pretty close to a whole kilogram here.

So it's definitely not just about 1/3 of a kilogram. 1/3 of a kilogram would be just one of these three equal sections. We're way more than that, so we rule that out. About one kilogram, that's what we saw.

When we take the 2/3 and add to that 3/8, where it looks like, and once again, we're estimating. We don't know exactly. It looks like we're a little bit over a kilogram, so I like this choice, and we're nowhere close to two kilograms. Two kilograms, we would be filling in another whole on top of this one right over here. So it's not that choice either.